In general, using a general purpose solver won't be 'optimal in execution time'. (And in general, we have no clue what the optimal execution time for any NP hard or NP complete problem is, because then we'd also have solved P vs NP.)
For some problems it’ll be optimal in execution time, for most it won’t be and you may be forced to let it approximate. But that’s usually still good enough.
Yes, it depends on your problem and your application. For some problems, you can approximate well, and in some applications that's good. And in some other applications it's fine to occasionally not solve a problem at all.
Comments
In general, using a general purpose solver won't be 'optimal in execution time'. (And in general, we have no clue what the optimal execution time for any NP hard or NP complete problem is, because then we'd also have solved P vs NP.)
Yes, it depends on your problem and your application. For some problems, you can approximate well, and in some applications that's good. And in some other applications it's fine to occasionally not solve a problem at all.